Abstract
In fibrous composites, tensile strength of reinforcements exhibits a stochastic nature, and the mechanical properties of the composites are significantly influenced by such strength variability. The present study aims at providing a comparative investigation of the influence of the statistical variation in fiber strength on the tensile properties of unidirectional composites reinforced by bamboo fibers. Monte-Carlo simulations coupled with the linear- and power-law Weibull distributions are performed to conduct numerical predictions for damage evolution and strength variability of the composites, and the predicted mean strength and failure strain are compared with the experimental results. The Weibull parameters used are achieved through the Maximum Likelihood Estimation with multiple data sets of fiber lengths. Fiber strength statistics is found to have an effect on composite mechanical properties. The results further indicate that the use of the power-law model is relatively efficient for modeling purposes in comparison to the linear-law model, which could be attributed to fiber diameter variation.
Highlights
Fibers are the main load-bearing constituents in fiber-reinforced polymeric composites and some of them exhibit brittle fracture behavior
In order to assess the accuracy of Multiple Data Set (MDS) estimates, the statistical parameters of the Weibull distribution are computed from the multiple data sets of fiber lengths for:
It is observed that there is a distinct difference in Weibull statistics at 20 mm gauge length, which may be attributed to a consideration of variable fiber diameter in the power-law model
Summary
Fibers are the main load-bearing constituents in fiber-reinforced polymeric composites and some of them exhibit brittle fracture behavior. Γ denotes the shape parameter and is an index of the variability of fiber strength: The strength distribution with a lower γ tends to perform larger scatter and vice versa This equation is termed as the linear-law Weibull (LLW) model that directly links fiber strength to its length. Compared to the linear-law model, the above-modified equation introduces an exponential parameter λ that accounts for the strength variability, which is caused by the change in inherent flaw distribution along a fiber and between fibers. Despite the importance of the Weibull distribution in reliability analysis of brittle materials, systematic contrastive study between the two models has not been conducted for explicitly linking the fiber strength variation to the composite strength distribution [3,22,23]. Weak-link scaling predictions for fiber strength is examined as well
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